Question

A farmer wants to build a fence around the edge

of a field shaped like a right-angled triangle, as
shown below. The fence costs £1.32 per metre.
Calculate the total cost of the fence.
Give your answer to the nearest pound.

Answer 1

£ 881

Explanation:

In a rt. triangle,

`sin(\theta)=(opposite)/(hypotenuse )\\\\cos(\theta)=(adjacent)/(hypotenuse )\\\\tan(\theta)=(opposite)/(adjacent)`

`tan(\theta)=(opposite)/(adjacent)\\\\\implies tan(56) = (x)/(154) \\\\\implies x = 154*tan(56)\\\\\implies x = 228.31`

`cos(\theta)=(adjacent)/(hypotenuse )\\\\\implies cos(56)=(154)/(y)\\\\\implies y = (154)/(cos(56)) \\\\\implies y = 275.4`

Perimeter = x+y+154

= 228.31 + 275.4 + 154

= 657.71

Fence required = 657.71 metre

cost per metre = 1.32

cost for 657.71 metre:

657.71 * 1.32

= 881.33

≈ 881